Borrowing the story of "making a horoscope", Professor Phan Thanh Nam discussed a question in mathematics: to what extent can current data be used to predict the future, and the limits of such predictions?.
When a child is born, many Vietnamese families record the exact date, time, month and year of birth to create a horoscope. "From a single point in time on the time axis, people seek to interpret their personality, future career, and even events that may occur throughout their lives," mathematician Phan Thanh Nam, professor at Ludwig Maximilian University Munich (Germany), shared in a talk on September 5 organized by the website Ray Sang in Hanoi. Here, Professor Nam borrowed a story from Vietnamese culture to talk about a core issue in science: extrapolation and prediction - from what is known in the present, how far can the future be predicted?
According to him, in mathematics, physics and data science, forecasts start from a measurement of the present, then use a model to infer what has not yet happened. If we fully know the state of a system at one time and know the laws that govern it, we can calculate its state in the future.
That is the spirit of extrapolation: taking what is known and extending it, deducing it into what is unknown. This approach is still useful and very popular. Scientists often rely on past data to forecast, from weather, population, epidemics, markets or the movement trends of particle systems in microphysics.
But that doesn't mean that having more current data means being able to look further into the future.
Professor Phan Thanh Nam explains the mathematics of taking current data to predict the future - to put it simply: "from one point you want to forecast the whole curve". If we stand at a point on the curve, we can know its value there. Knowing the first derivative, we know how fast the curve is going up or down. Knowing the second derivative, we know how it is curving. Higher order derivatives continue to provide more detailed information.
But extrapolation does not mean that a bridge can extend indefinitely. A rule may be very true in one scope but no longer be true when moving to another scope. A model may predict accurately over a certain period of time but becomes less reliable over time. A trend may be stable for many years but suddenly change when system conditions change.
Therefore, whether the forecast is accurate or not always depends on the data collected, the scale and the point of view of the measurer, Professor Phan Thanh Nam said.
According to him, this also poses problems with the way people view life. People often take something that happened in the past, explain it with a rule or belief, and then assume that rule will continue to hold true in the future. Meanwhile, "extrapolation is not always universal".
Limits of measurements
Also mentioning horoscopes, Professor Tran Xuan Hoai, former Director of the Institute of Applied Physics, Vietnam Academy of Science and Technology, gave the example of two people born on the same day and at the same time, but had completely different life circumstances and later fates. At that time, if you want to explain the difference, the horoscope reader must update the place of birth, family situation and many other information.
This is not just a horoscope story. It is also a basic principle of science and in life, if the initial data do not contain enough information about a system, we cannot expect them to allow us to accurately predict that entire system.
One person may have the same birthday as another person, but life is also shaped by education, living environment, economic conditions, relationships, personal choices and countless other factors. This is similar in science: a model built from past data is often based on the assumption that observed regularities will continue to hold, but in reality, initial conditions can change, new factors can emerge, and a system can transition to a different state. That's why long-term forecasting is always more difficult than short-term forecasting in many complex systems.
Another difficulty is that the future does not necessarily preserve the conditions of the present. This is especially important when talking about measurements. In science, there is no measurement that gives us the whole of reality. Each measurement observes only one aspect, at one resolution and with a certain level of precision.
According to Professor Phan Thanh Nam, the important thing in science is to always be transparent about what data, what model a prediction is based on, how accurate it is, what the limits of measurement are, and whether it is verifiable or not. On the contrary, statements that lack these conditions can be considered pseudoscience.
Science does not require predictions to always be correct. It is important that the forecast must have a basis, be verifiable, and clearly state the conditions for it to remain trustworthy.
Therefore, extrapolation is not useless. On the contrary, it is one of the important tools of science. But extrapolation is only meaningful when we know what conditions it is based on, to what extent it is true, and how reliable it is.
